The measurement of oxygen gas by its paramagnetic property is a well established technique which is approved for many industrial and medical applications, where it generally provides excellent selectivity, accuracy and reliability. This is because oxygen is one of the few gases which exhibit paramagnetism, meaning it will be strongly attracted by a magnetic field. Most other common gases are diamagnetic, which is a very much weaker magnetic effect.
The force Fm that acts on a spherical test body in an inhomogeneous magnetic field is proportional to its volume V, the magnetic field gradient HdH/dz and the volume magnetic susceptibility difference between the test body X1 and surrounding sample gas X2 (see “The magnetic susceptibility of nitrogen dioxide”, G G Havens, Phys. Rev. vol 41 (1932) pp. 337-344). That is:Fm∝V*H*dH/dz*(X1−X2)
Since the volume magnetic susceptibility of the sample gas is proportional to the sample gas density, the force is proportional to the partial pressure of oxygen. The volume magnetic susceptibility of oxygen at room temperature is 1.9×10−6 SI units, whereas nitrogen (a typical background gas) is −6.7×10−9 SI units. Therefore the force due to oxygen in the gas mixture, even small amounts, is substantially larger than other gas components, hence the excellent selectivity of this measurement principle to oxygen.
The force itself is quite weak, typically a few micro-Newtons with pure oxygen for magnetic field strengths and test body volumes that can be practically achieved. Consequently a very sensitive system is required to measure this force with the necessary resolution required for oxygen sensing applications.
The typically preferred arrangement uses a magnetic susceptibility torsion balance inside a sealed cell which is arranged to admit the sample gas. The torsion balance comprises a test body having a particular shape, and filled with a diamagnetic gas such as nitrogen. The body is suspended in a non-uniform magnetic field in the sealed cell, and is typically balanced by initially filling the cell with nitrogen. When the cell is subsequently filled with a test gas containing oxygen, the paramagnetic oxygen gas is attracted to the stronger part of the magnetic field, and the test body rotates. This rotation is detected and used to indicate the oxygen content of the sample gas.
Such a device was first described by Havens (see reference above) who carefully studied the factors that govern sensitivity of the test body, in particular its shape, finding that a sphere is optimum. Other magnetic susceptibility torsion balances using different test bodies have been examined as early as 1850 (Faraday M (1851), Proc. R. Inst., vol. 1, p. 229). However, they did not match the sensitivity achieved by Havens.
The first commercial oxygen analyser using a magnetic susceptibility torsion balance was developed by Pauling, Wood and Sturdivant under US government contract NDCrc-38 (J. Am. Chem. Soc. 68 (1946), 795) and is disclosed in U.S. Pat. No. 2,416,344 (application filed 23 Aug. 1941). The test body consists of a pair of identical hollow glass spheres on either end of a rigid bar that is suspended by a fine glass fibre under tension, which provides a very soft torsion spring constant. The spheres are made as light as possible so the inertia is not much larger than the magnetic force, and balancing weights are also added to minimise the effect of orientation sensitivity. This assembly is placed between magnet poles that generate a strong magnetic field gradient and arranged so the force acting on both spheres reinforces the torque.
Movement of the test body is detected using an optical lever. This consists of a light source that makes a beam of light which reflects off a mirror at the centre of the test body and then onto an optical readout, which indicates displacement of the subtended beam. The beam displacement at the optical readout is proportional to the angular movement of the test body and the length of the optical lever arm, i.e. the distance between the mirror and the readout. Therefore good angular resolution may be obtained by increasing the optical lever arm length as necessary while maintaining focus of the beam spot on the readout.
The optical lever is also advantageous for rejecting errors due to rectilinear motion and vibration, as the angular movement is detected from the centre of a balanced test body that is only allowed to rotate about its principal axis.
Later inventions made significant improvements to the manufacturability and performance of magnetic susceptibility torsion balances, in particular through the use of an electronic optical lever to detect and control motion of the test body using a feedback system. Munday in GB 746,778 discloses an optical lever feedback system in which a photo-electric cell is used as the optical readout and a wire coil, attached around the test body that conducts via the suspending wire, is used to provide feedback. The system keeps the test body at a null position by reacting to motion of the test body. By maintaining the test body substantially in the same position in this way, all measurements can be recorded at the position of maximum sensitivity. This is achieved by amplifying the photo-electric cell signal to generate a current in the wire coil that produces a magnetic torque equal and opposite to the perturbing force that would otherwise push the test body away from its null position, i.e. the magnetic force due to a change of the amount of oxygen in the sample gas. This current can then be measured in order to determine the magnetic force, and hence the oxygen content of the sample gas. A similar system is disclosed by U.S. Pat. No. 3,026,472, but feedback is provided by electrostatic actuation of the test body.
Many modern oxygen sensors still use the optical lever with refinements. For example, “Highly accurate measurement of oxygen using a paramagnetic gas sensor”, R P Kovacich, N A Martin, M G Clift, C Stocks, I Gaskin, J Hobby, Measurement Science and Technology, vol 17 (2006), pp. 1579-1585) describes an optical lever with a solid state source (light emitting diode) in place of an incandescent one and a pair of photo-diodes connected in reverse polarity to provide a zero voltage null position when both photo-diodes are equally illuminated, i.e. when the beam spot centre is exactly in between the photo-diodes. Using a pair of photo-diodes also has the advantage of rejecting common mode errors, such as intensity fluctuations of the light source. This electronic optical lever feedback system gives much improved sensitivity, linearity and stability.
Several inventions have tried using arrangements without the optical lever, such as an electrostatic sensing and actuation system as disclosed in U.S. Pat. No. 3,612,991 and an oscillating magneto-dynamic system as disclosed in U.S. Pat. No. 6,246,227. However, both have disadvantages. The electrostatic system requires gold plating of the test body which makes manufacture difficult, requires high voltages (up to 100 Volts) thus limiting compact electronic design, and is not as corrosion resistant as other metals such as platinum. Most plating metals are not suitable as they tend to be paramagnetic or prone to corrosion. The oscillating system is disadvantaged by cross sensitivity to gases with a significantly different viscosity to molecular weight ratio, such as helium and halocarbons with heavy molecular weight; gases which are used as anaesthetic agents.
A diffusion based device can be designed to give a high precision oxygen measurement (typically <0.2% Oxygen or better accuracy) with low sample flow rate dependence. However, certain applications, such as those in medical anaesthesia or pulmonary function testing, require a fast response to any change in the oxygen concentration level. This in turn requires a fast sweep of the gas volume in the vicinity of the nitrogen filled spheres and hence a direct flow of gas through the measurement cell and a minimisation of internal volume. However, any such motion of the gas will have a momentum impact on the spheres and this can appear as noise on the signal due to induced oscillatory forces and potentially a signal bias unless the system is perfectly symmetric with respect to gas flow regime and sphere morphology and construction. In short, there can be a strong dependence of signal with flow rate as the price to pay for a fast time response—they are coupled parameters and cannot easily be minimised simultaneously.
In an effort to reduce the dependence of signal with flow rate for devices with fast response times, previous designs such as U.S. Pat. Nos. 4,988,946 and 7,102,346 have attempted to reduce as much as possible all asymmetry in the flow path and tried to shield the test body from direct or large magnitude velocity vectors by controlling the incoming gas direction and type of flow past the suspension test body. However, the internal asymmetry can never be reduced to zero due to normal manufacturing tolerances and essential asymmetrical features such as magnets, test body and mounting. Similarly, the flow past the test body can never be reduced to zero as the gas must flow through the device. This prior art will now be discussed in more detail, although the magnetic fields and optical feedback systems used in the measurements will not be discussed here—only the design of the gas flow regime within the devices to reduce the asymmetry and flow momentum impact on the test body. FIG. 1 shows a cross-section through an apparatus that is shown and described in U.S. Pat. No. 4,988,946, in order to illustrate the gas flow regime. In this case, the test body (120) consists of a dumb-bell arrangement with hollow glass spheres filled with nitrogen, a mirror, a feedback coil and a suspension strip. The incoming gas enters via twin inlet pipes (109) used in a symmetrical configuration so as to sweep the measurement chamber and also to reduce disturbance of the test body (120) by virtue of halving the speed of gas impinging on the dumbbell (131) and attempting to equalise it by the simultaneous arrival from both sides. The inlet pipes are also positioned so as to admit the gas directly aimed at the spring (118) to which the suspension strip (119) is welded and which is situated in a very small space. The incoming gas turns and runs along the channel (108) which houses the suspension strip (119). Upon arrival to the middle part of the chamber, the gas turns towards the outlet pipe (110) and emerges out of the chamber. The outlet includes a restrictor (111) which is chosen so as to stop the immediate turning of the gas to the outlet from its emergence from the channels (108) (which would leave the gas in the front of the mid-chamber (124) to exchange by diffusion, which is slow). When the restrictor is chosen correctly, the pressure built up in the rear part of the mid-chamber (125) ensures that part of the gas turns towards the front part (124) and sweeps it and thus a fast response time is achieved.
FIG. 2 shows a cross section through an apparatus that is shown and described in U.S. Pat. No. 7,102,346, in order to illustrate the flow regime. The test body is a similar arrangement to that in FIG. 1. The gas sample enters via ports (201) (arrows A). The inlet ports are of narrow diameter to reduce any smearing of concentration changes in the gas flow. At the front of the device, the gas is forced to undergo a ninety degree turn (arrows B) to enter a narrow channel (202) defined between the body (205) and the face plate (207). This in turn breaks up the gas flow and causes the flow channel (202) to have a wide distribution of momentum and to consist of very small vortices. The gas enters the measuring chamber (203), where the large increase in cross section causes the flow per unit area to fall significantly. The test body (211) is mounted as shown such that it lies parallel to and in symmetrical relation to the narrow channel (202). The gas then flows past the test body (211) (arrows C). Due to these fine vortices within the flow and the symmetrical flow across either side of the test body, the net force on the test body is small and hence the influence of any change in flow rate is lower than would be otherwise. Furthermore, as the measurement chamber is actually being swept by the gas flow, any change in sample concentration occurs rapidly compared to diffusion. After passing through the measurement chamber, the gas enters the exhaust port (204) (arrow D) accelerating the gas flow. The exhaust port is preferentially of larger diameter than the inlet ports to permit any chaotic flow to be rapidly expelled. An extended gap at the back of the chamber compared to the front also reduces the effect of any turbulence generated as the sample enters the smaller outlet bore. The overall effect is that a fast time response with acceptable flow error is achieved.